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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Unknotted homology classes on unknotted surfaces in $ S\sp 3$

Author: Bruce Trace
Journal: Trans. Amer. Math. Soc. 318 (1990), 43-56
MSC: Primary 57M99; Secondary 57M25
MathSciNet review: 965303
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Abstract: Suppose $ F$ is a closed, genus $ g$ surface which is standardly embedded in $ {S^3}$. Let $ \gamma $ denote a primitive element in $ {H_1}(F)$ which satisfies $ {\theta _F}(\gamma ,\gamma ) = 0$ where $ {\theta _F}$ is the Seifert pairing on $ F$. We obtain a number theoretic condition which is equivalent to $ \gamma $ being realizable by a curve (in $ F$) which is unknotted in $ {S^3}$. Various related observations are included.

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PII: S 0002-9947(1990)0965303-9
Article copyright: © Copyright 1990 American Mathematical Society

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